A high-performance method is proposed for solving a linear system in the shielding current analysis of a cracked superconducting film. After discretized with respect to time and space, the initial-boundary-value problem of the shielding current density reduces to a linear system at each iteration cycle of the Newton method. Although the linear system can be easily solved with GMRES, the number of elements adjacent to cracks strongly affects convergence property. In order to improve convergence property of GMRES, an efficient method is proposed and its performance is numerically investigated.